I'm considering 1 & 2 Samuel and 1 Chronicles together because they cover the same main subject – the life and times of David. Volumes have been written about David and I can't possibly cover him in one quick blog post. However, if you undertake this study there are a number of different ways to approach it.
Character study – David's life divides into three phases: Shepherd, Renegade and King. What kind of man is he? How does he grow and change through each phase? What is the dominant aspect of his relationship with God during each phase?
David's triumphs and failures – He had plenty of both. Note how he responds to God in each situation.
A who/what study – Who does David come in contact with? What happens? What does he take away from the encounter?
David's prayers – What prompts the prayer? What does he say about God? What does he ask for?
Consequences – None of these books shy away from portraying sin or its effects. Keep track of the sins – not only of David, but others like Eli, and Saul – and how the individual sins impact others and even the nation itself.
If you're really ambitious, follow your footnotes and read the Psalms that are cross-referenced to the events in David's life. This gives a uniquely intimate look at his relationship with God. I love being able to look at his "journal". Also the range of emotions he records is reassuring.
David's walk with God wasn't all hearts and rainbows, and by allowing us to see his failures as plainly as his great victories, we see God's mercy and grace on full display.
What's your favorite story about David?